Representing expectation values of projectors as series for evolution reconstruction

Representing expectation values of projectors as series for evolution reconstruction
Zhou, Hua; Wang, Rong; Zhu, Yong; Su, Yang; Xu, Zhiyong; Wang, Jingyuan; Shen, Huiping; Li, Jianhua; Xiang, Peng; Zhang, Baofu
2016-09-28 00:00:00
We propose a Hamiltonian-independent approach for evolution reconstruction, which reconstructs the density operator of an evolving quantum system on the basis of recovering its time-varying expectation values of projectors. We represent band-limited expectation values of projectors as series, in which the coefficient of each term is a sum of an infinite set of measurement results. Both of the series for multiple measurement records and for a single record are given. We demonstrate using them to recover an expectation value and reconstruct the density operator of an evolving two-dimensional quantum system. The theoretical and simulative results prove that the two series are effective when performing a small number of measurements. Our approach is applicable to any quantum system of countable dimensions with arbitrary Hamiltonian.
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Representing expectation values of projectors as series for evolution reconstruction